Advanced PEBA-based membranes for enhanced removal of volatile organic compounds from wastewater

Abstract

The removal of volatile organic compounds (VOCs) from aqueous streams is of considerable environmental and public-health importance. In the present work, nanocomposite membranes were fabricated by incorporating CaF₂ nanocrystals into a poly(ether-b-amide) (PEBA) matrix and evaluated for the hydrophobic pervaporation (PV) of (1-methylethyl)benzene (1-MEB) from dilute aqueous solutions. Relative to Pure PEBA membrane, the introduction of CaF₂ nanocrystals produced pronounced changes in the physicochemical properties of the membranes. The water contact angle (CA) increased to a maximum of 108.77° at 0.5 wt% loading, the degree of swelling (DS) declined from 25.99% to 12.5%, fractional free volume (FFV) were reduced, and mechanical properties were enhanced at optimal nanocrystal contents. These modifications resulted in substantially improved separation performance: at 1 wt% CaF₂ the separation factor rose from 82.51 to 63330.16, water flux decreased from 721.5 to 7.5 g m⁻² h⁻¹, and 1-MEB flux increased to 23.75 g m⁻² h⁻¹.

To gain deeper insight into the interaction between the feed components and the prepared membranes, Hansen solubility parameters (HSP) were applied, and modified Bagley relationship incorporating the agglomeration index was introduced to calculate the HSP of nanocomposites. The modified HSP provided a reliable explanation for the variations observed in the membrane properties at different nanofiller loadings.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s11671-026-04954-3.

Introduction

1-Methylethylbenzene (1-MEB) is a volatile organic compound (VOC) contributing to environmental pollution [1]. It is found in industrial wastewater, crude oil (0.1 wt%), and petrol (0.14–0.51 vol%) [1, 2]. Its concentrations near paint and petrochemical factories reach 1.581 mg/L and 0.36 mg/L, respectively [1, 3]. Exposure to high levels can cause neurological symptoms and irritation to the skin and eyes in humans and animals [1–3].

As a result of the environmental and health issues discussed above, VOCs, including 1-MEB, should be separated from their emission sources. VOC removal can be achieved using a variety of separation processes, such as biological degradation, membrane technology, catalytic oxidation, and distillation [4]. Being cost-effective and energy-efficient, membrane processes are a preferred choice [5–7]. In most cases, VOCs can be removed via polymeric pervaporation (PV) membranes [8]. In this regard, a variety of polymers, including nitrile rubber (NR), styrene-butadiene rubber (SBR), poly [bis (phenoxy) phosphazene] (BPOP), polydimethylsiloxane (PDMS), polyphenylsulfone (PPSU), ethylene propylene diene monomer (EPDM), polyvinylidene fluoride (PVDF), and poly (vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) have been applied as PV membrane material [9, 10].

PEBA is a thermoplastic elastomer (TPE) copolymer composed of rigid and flexible blocks [11]. Polyamide hard blocks generate physical crosslinks, whereas flexible soft polyether blocks act as entropic springs [11]. This results in a two-phase morphology with crystalline polyamide (PA) and amorphous polyether (PE) domains. In other words, PEBA can bridge the gap between thermoplastics and elastomers due to its high flexibility [11, 12]. PEBA offers good chemical resistance, flexibility, and good dynamic properties even at low temperatures [11]. PEBA is produced in several grades, including Pebax 2533, 3533, 4033, 5533, 6333, and 7033. Among these grades, those with more flexible PE segments exhibit higher hydrophobicity [13]. Accordingly, compared to other grades, Pebax-2533 (Fig. S1) has the highest PE content (80 wt%) [13] and thus, the highest hydrophobicity.

Several methods are currently available for modifying membrane surface and structure [7]. However, studies showed that adding nanofillers can improve PEBA PV membranes [14]. In this regard, fluorinated fillers are one group of nanofillers whose fluorine atoms contribute to the increased hydrophobicity of the resultant nanocomposite [15]. Among alkaline earth fluorides, calcium fluoride (CaF₂) (Fig. S1) is a well-known nanocrystal containing calcium and fluorine ions. In the structure of this material, there are eight ions adjacent to each Ca²⁺ and four Ca²⁺ ions surrounding each F⁻ in its centered cubic unit cell [16]. This nanocrystal has excellent properties such as sufficient hardness and high thermal stability and high thermal stability [16]. Aside from being cost-effective, it has a chemically stable and non-hygroscopic structure [16]. CaF₂ is widely utilized in optical devices, batteries, catalysts, and also as a coating and additive [16]. However, its application in the fabrication of filtration membranes as well as PV membranes has not been explored yet. Since the fluorine atoms in CaF₂ bring about low surface energy and high hydrophobicity, the incorporation of this material into polymeric membranes can increase membrane hydrophobicity.

The selection of CaF₂ as the nanofiller was motivated by its unique combination of properties that address specific limitations of conventional fillers in hydrophobic PV. Unlike inherently hydrophilic SiO₂ and TiO₂, which require surface modification with hydrophobic agents to repel water, CaF₂ is intrinsically hydrophobic. Furthermore, while hydrophobic zeolites and surface-functionalized MOFs have been explored for this purpose, their synthesis predominantly relies on bottom-up routes that are complex, costly, and difficult to scale industrially. In contrast, CaF₂ is commercially abundant and cost-effective; approximately 9.5–10 million tons are produced annually worldwide, and its nanocrystalline form can be readily obtained via top-down mechanical milling—a simple, scalable, and industrially viable approach [17]. Consequently, CaF₂ does not require additional hydrophobic modification, nor does it suffer from the batch-to-batch variability and high cost associated with engineered hydrophobic fillers. These characteristics collectively render CaF₂ a practical, economical, and advantageous alternative for enhancing the hydrophobicity and separation performance of PEBA-based PV membranes.

The conventional Bagley relationship (Eq. 9) is widely used to estimate the HSP of polymer–nanofiller composites. However, this approach assumes ideal filler dispersion, which is practically unattainable due to inevitable agglomeration [18]. Other predictive strategies, such as group contribution methods and topological approaches, similarly treat the composite as a homogeneous phase without accounting for filler agglomeration [19, 20]. A comparison of these methodologies is provided in Supplementary Table S1. To overcome this limitation, the present study introduces, for the first time, a modified Bagley relationship that incorporates the Suetsugu dispersion index to account for non-ideal filler distribution.

This study is the first to use CaF₂ nanocrystals in fabricating nanocomposite PV membranes. CAF₂ nanocrystals were obtained through a mechanical milling process and incorporated into the PEBA membrane matrix to improve its hydrophobicity. The resultant membranes were characterized via different methods, and their performance was investigated in the separation of 1-MEB from water. Additionally, because the HSP distance does not reliably correlate with changes in membrane properties—such as CA, swelling degree, sorption selectivity, and PV fluxes—a novel method was proposed in this study to adjust the HSP of nanocomposites by accounting for nanofiller agglomeration.

Materials and methods

Materials

Polyether block amide (PEBA, Pebax 2533 SN 01), having PA/PE of 20/80, was obtained from Arkema (France). Dimethylacetamide (DMAc) with 97% purity was purchased from Merck (Germany). CaF₂ powder (particle size = 1 μm) was obtained from Tooma Minerals Co. (Iran), and (1-methyl ethyl) benzene (1-MEB) with 99.99% purity was provided by PROLABO (UK).

Preparation of nanocrystals and membranes

CaF₂ nanocrystals

CaF₂ powder was ball milled in 100 mL stainless steel jars using a commercial planetary mill (NARYA-MTM-2 × 250 H, Amin Asia Fanavar Pars, Iran) at 600 rpm in an air atmosphere. Ball milling was conducted in two stages: (1) a CaF₂ powder-to-ball weight ratio of 2:15 for 4 h, followed by (2) a CaF₂ powder-to-ball weight ratio of 1:15 for 16 h.

PEBA and PEBA/CAF₂ nanocomposite membrane

A polymer solution with 12.5 wt% concentration was obtained by adding PEBA to DMAc, followed by stirring at 85 °C for 1 h. The solution was degassed, cast on a glass plate, and dried in a 50 °C oven for 24 h. A schematic diagram for the mentioned procedure is depicted in Fig. S2(a).

As shown in Fig. S2(b), CaF₂ nanocrystals were dispersed in DMAc through 1 h bath ultrasonication (200 W, 40 kHz, Grainger PS-30 A, China) at room temperature and then 5 min probe ultrasonication (400 W, 24 kHz, Hielscher UP400S, Germany). Afterward, the proper amount of PEBA was added to the dispersion to obtain a solution containing 12.5 wt% polymer concentration. After stirring at 85 °C for 1 h, degassing, casting, and drying were conducted as mentioned above. Depending on the concentration of CaF₂ nanocrystals (0, 0.5, 1.0, and 1.5 wt%) in the casting solution, membranes were labeled as PEBA-0, PEBA-0.5, PEBA-1, and PEBA-1.5.

Characterization

CaF₂ nanocrystals were characterized using transmission electron microscopy (TEM). After dispersion in DMAc by stirring and sonication, samples were prepared on copper grids coated with carbon-Formvar. Imaging was performed using a LEO 912ab TEM (Zeiss, Germany) at 4000× magnification and an acceleration voltage of 120 kV. Nanocrystal diameters were analyzed with ImageJ software, and a size distribution histogram was generated. The membranes were characterized using field emission scanning electron microscopy (FESEM, MIRA3, TESCAN, Czech Republic). Samples (2 cm × 2 cm) were freeze-fractured in liquid nitrogen for cross-sectional analysis and sputter-coated with Au-Pd for 180 s at 20 mA using a Quorum coater (Q150R-ES, USA). Elemental surface composition was also analyzed using an energy-dispersive X-ray (EDX) spectrometer attached to the FESEM. In addition, to investigate the spatial distribution of CaF₂ across the membrane thickness, EDX analyses were performed at multiple locations along the cross-section, including regions close to the membrane surface and within the bulk. Nanoparticle dispersity in a polymeric matrix was calculated using FESEM analysis. Surface images of PEBA-0.5, PEBA-1, and PEBA-1.5 membrane samples were inspected using ImageJ software. For each membrane composition, three FESEM surface images from different regions of the sample were analyzed. The Suetsugu agglomeration index (A_i) for nanofillers was then determined as described below [21]:

1

In this model, , , _i, and correspond to the observation area (µm²), volume fraction (vol%), number of agglomerates, and their diameter (µm), respectively. The dispersion index () was obtained based on as follows [21]:

2

=0 represents the poorest dispersion when all nanoparticles are agglomerated, and =1 shows the ideal distribution, with the most uniform dispersion of nanofillers [21]. The A_i was calculated as the mean value across these three images and is reported as mean ± SD. Roughness of the fabricated membranes was determined through atomic force microscopy (AFM, Ara Research, Iran). Three separate points were probed on each membrane sample, and the obtained results were processed by image processing software to estimate the area factor (), root mean square surface roughness (, nm), and average surface roughness (, nm). The roughness ratio ( r) was calculated by the equation below [22]:

3

Fourier transform infrared (FTIR) spectroscopy was employed to analyze both CaF₂ nanocrystals and the fabricated membranes. The spectra were obtained on an Avatar 370 (Thermo Nicolet, USA) apparatus through 32 scans and 32 background scans in the wavenumber range of 500 cm^− 1 −4000 cm^− 1. X-ray diffraction (XRD) spectra of CaF₂ nanocrystals and fabricated membranes were collected on an EXP01 16015 device (GNR Explorer, Italy) using Cu-Kα radiation in the 2θ range of 5–60° with a step size of 0.05˚ and a step rate of 1˚/s. The crystallinity degree ( was determined using the OriginPro software, and crystallite size ( L, Å) was calculated by the Scherrer Eq. [1]. Estimation of the interlayer spacing between lattice planes was also carried out using Bragg’s law [1]:

4

where  n is the reflecting order , and  d represents d-spacing (Å).

Membrane thermal properties, including melting point (), melting enthalpy (), and glass transition temperature (), were assessed through differential scanning calorimetry (DSC). The heating-cooling-heating cycle was performed using the METTLER TOLEDO (Switzerland) equipment under an N₂ flow of 50 mL/min and a 10 °C/min heating rate. The second heating thermogram was utilized to calculate the mentioned parameters. Using the melting enthalpy of 100% crystalline PEBA-2533 ( of PE phase = 166.4 J/g and of PA phase = 230 J/g), the following equation was implemented to determine the crystallinity degree () for each phase [23]:

5

Then the total crystallinity of the membrane () was determined as below [23]:

6

and represent the degree of crystallinity of PE and PA segments, respectively.

Tensile properties of membranes were measured using an STM-20 universal testing machine (Santam, Iran) with a 6 kg load cell. Following ASTM D882-18 requirements, the dimensions of rectangular specimens were 10 mm × 70 mm, and the crosshead speed was 500 mm/min. Positron annihilation lifetime spectroscopy (PALS) was used to measure the fractional free volume (FFV) of PEBA membranes. The setup included two plastic scintillation detectors, a ²²Na radioactive source (0.74 MBq) sealed between 12 μm Kapton sheets, and a CAEN DT5730 digital data logger. The source was placed between two identical membrane samples, and positron lifetimes were recorded using a fast-fast coincidence spectrometer. The resulting spectra were processed with MATLAB and analyzed using LT-10 software to determine positron lifetimes and intensities. Based on the lifetime (τ₃, ns) and intensity (I₃, %), the mean free-volume hole radius (R, Å) and FFV (%) were calculated using semi-empirical methods [24]. Water contact angle (CA) and glycerol CA with the membrane surface were determined using the CA instrument with a 4 µl droplet size and 1 µl/s of dosing speed. Images of at least four droplets on each sample were analyzed, and the average of the collected data was recorded as apparent or Wenzel CA. The ideal surface CA known as the Young or ideal CA can be obtained using the Wenzel equation as follows [25]:

7

, , and  r represent the apparent CA, Young CA, and roughness ratio, respectively.

The solution-diffusion theory was utilized to investigate the solution, diffusion, and desorption stages during PV [26]. Sorption into the membrane is related to the affinity between the polymeric membrane and feed component, which can be defined by the HSP distance (∆, /or ), shown below [18]:

8

where and symbolize dispersion interaction /, and represent polar force factor /, and and denote the hydrogen bonding interaction force factor /for the membrane and the feed component respectively. Greater interactions between the polymer and the component are indicated by a smaller value of ∆ [18]. For binary mixtures such as a nanocomposite membrane or a feed solution, the modified HSP should be calculated in order to estimate the solubility values. Regarding this, the Bagley method is the most applicable way to obtain HSP parameters [18]:

9

where and refer to the HSP values for the first and second components (e.g., polymer and nanoparticle in the membrane matrix), while  a and  b represent their relative contents. The HSP parameters for CaF₂ were determined using HSPIP v.5 software and are presented in Table 1 along with HSP parameters of the materials utilized in these experiments.

Table 1.

HSP parameters

Material	(MPa)1/2	(MPa)1/2	(MPa)1/2	Reference
PEBA-2533	17.6	7.6	6.8	[13]
CaF2	109.8	0	16.5	-
1-MEB	18.1	1.2	1.2	[27]
Water	15.5	16	42.3	[13]

The Bagley relationship (Eq. 9) can be applied in the case of ideal nanomaterial dispersion in a polymer matrix; however, due to nanoparticle agglomeration, the Bagley solubility equation needs to be modified. Therefore, a method was proposed in the present study to modify the HSP parameters of nanocomposites regarding the agglomeration of nanofiller. In this case, the modified HSP parameters were calculated based on the determined from FESEM analysis. For a membrane composed of a polymer and nanoparticles, the modified nanoparticle content and polymer content were calculated by multiplying the by the nanoparticle ( a) and polymer content ( b) of each membrane sample as follows:

10

11

Therefore, the modified Bagley correlation based on modified compositions is as follows:

(12)

where , , and represent the new HSP values based on the modified compositions of the membrane matrix. Finally, modified Δ was calculated based on the new parameters obtained from the modified Bagley correlation.

To study the degree of swelling (DS) at room temperature, the dry weight () of membranes was recorded prior to immersing them in an aqueous solution containing 50 ppm 1-MEB. Swollen membranes were taken out of the feed every 48 h to be reweighted () after removing excess liquid droplets. The process lasted for several days until no considerable weight change in two consecutive tests was observed. As a final step, the DS for swollen membranes was calculated using the following equation [18]:

13

To determine the sorption and diffusion selectivity of the fabricated membranes, all membrane samples were weighed and transferred to sealed jars of an aqueous solution containing 50 ppm 1-MEB. The membranes were kept in the feed solution at 25 °C to achieve sorption stability. Then, they were reweighed. Moreover, the concentration of the remaining 1-MEB solution was measured by a UV/visible spectrophotometer (SP-UV-300SRB, Germany). Based on mass balance, the amount of 1-MEB and water uptake and their concentrations in the membrane were calculated. Then, by applying the following equations, sorption () and diffusion selectivity () were obtained [28]:

14

15

where and represent the concentrations of 1-MEB and water in the initial feed solution, respectively, while and reflect their concentrations in the membranes.

PV experiments

The laboratory setup applied in PV experiments is illustrated in Fig. S3. The setup includes a feed container, a disk-shaped cross-flow membrane module, a feed circulation pump (KJ 2000, Kojine Co, Taiwan), a vacuum pump (DV-6E Eliminator, USA), a pressure gauge, a cold trap, and a liquid nitrogen tank. The PV experiments were carried out by adding a solution of 50 ppm 1-MEB in water to the feed container, followed by sealing the container to avoid VOC loss. Membrane samples with 0.0016 m² effective area were introduced to the stainless steel membrane module. PV feed was pumped into the module at 25 °C, crossed the membrane surface, and was recycled back to the feed container. After a while, the vacuum pump was switched on. As the feed circulation was ongoing, the vacuum valve was opened to provide a vacuum level of 15 mmHg, and the test was started. The process was continued, during which the feed components passed across the membrane, evaporated, and then were captured by a cold trap submerged in the liquid nitrogen tank. Finally, the pumps were turned off, and the weight of the trap that collected condensed permeate was measured. Cold trap weight before and after the PV process was utilized to calculate the weight of the gathered permeate.

PV performance was reported by applying the following equations to calculate permeation flux ( J, g/m²h), separation factor (), and PV separation index ( PSI) [1, 18]:

16

where  Q stands for the permeate mass (g),  A is the membrane effective area (m²), and represents the duration of the PV test (h).

To estimate the concentration of 1-MEB in the permeate, a UV-Visible spectrophotometer was utilized, and was derived as follows [1, 18]:

17

where  X and  Y correspond to the weight fractions of components in the permeate and feed, respectively, while  i and  j represent 1-MEB and water, respectively.  PSI (g/m²h) was then calculated based on the equation below [1, 18]:

18

Results and discussion

Morphology of CaF₂ nanocrystals

The morphology of CaF₂ nanocrystals was studied by TEM, and the obtained image is shown in Fig. 1(a). The TEM image shows that the CaF₂ nanocrystals are spherical with homogeneous size distribution. Figures 1(b) and 1(c) indicate the particle size and surface area distribution histograms derived from the TEM image, respectively. According to the results, the mean diameter of CaF₂ nanocrystals is 246.70 ± 40.55 nm, and their average surface area is 50958.70 ± 13786.05 nm².

Fig. 1.

a. TEM image, b. size distribution, and c. surface area distribution of CaF₂ nanocrystals

Morphology of membranes

The surface and cross-sectional FESEM images of the PEBA-0 membrane and its nanocomposites are depicted in Fig. 2. As shown in this figure, the thickness of all membranes is in the range of 20–30 μm. The surface images confirm that all samples are pore-free, and the cross-sectional images reveal a dense and symmetrical morphology, which makes them appropriate for the PV process [29]. According to Fig. 2(b), nanocrystals are dispersed uniformly in PEBA-0.5; however, as the concentration of CaF₂ increased, nanocrystal agglomeration became apparent. Agglomeration of nanocrystals can also be quantified using the and parameters listed in Table 2. As shown in this table, nanocrystals exhibited the highest dispersity within PEBA-0.5 compared to PEBA-1 and PEBA-1.5, with values of of 0.57 and of 0.43. However, PEBA-1.5 has the lowest (0.03), indicating significant nanocrystal agglomeration within the membrane structure.

Fig. 2.

Surface and cross-sectional FESEM images and EDX spectra of a. PEBA-0, b. PEBA-0.5, c. PEBA-1, and d. PEBA-1.5 membranes (yellow arrows indicate the surface points analyzed by EDX)

Table 2.

Agglomeration (A_i) and dispersion (D_i) indices of nanocomposite membranes

Membrane
PEBA-0.5	0.43 ± 0.01	0.57 ± 0.01
PEBA-1	0.73 ± 0.02	0.27 ± 0.02
PEBA-1.5	0.97 ± 0.04	0.03 ± 0.04

Surface elements of membranes

The EDX spectra of the membranes are illustrated in Fig. 2. Carbon and oxygen peaks are evident in the EDX spectra of all membranes and correspond to the chemical structure of PEBA. The silicon peak in all spectra can be assigned to dust particles or impurities on the membrane surface. Calcium and fluorine peaks appeared in the spectra of nanocomposite membranes, and their intensity increased at higher CaF₂ loading.

To further investigate the distribution of CaF₂, cross-sectional EDX analyses were performed at different regions from the near-surface to the bulk of the membranes, as presented in Fig. S4. The Ca and F contents increased with increasing CaF₂ loading and were also detected in the bulk region, while for PEBA-1.5, their contents were higher in the bulk than near the surface, supporting the migration of CaF₂ nanocrystals from the surface toward the bulk at higher loading [30].

Topography of membranes

The surface topography of the prepared membranes was investigated, and the obtained AFM images are shown in Fig. S5. Roughness parameters including , ,  r, and were calculated and tabulated in Table S2. Results indicate that PEBA-0 accounts for the lowest roughness parameters (, , , and  r=1.001), and with increasing CaF₂ loading up to 1 wt% in the membrane matrix, the mentioned parameters increased so that the highest values were recorded for PEBA-1 (, , , and  r=1.064). However, as the CaF₂ concentration increased to 1.5 wt%, roughness parameters decreased due to the significant agglomeration of nanocrystals and their migration from the surface to the bulk of the membrane [30]. AFM observations are consistent with surface FESEM images (Fig. 2), A_i and D_i data (Table 2), and findings of other studies [31].

Chemical structure

As illustrated in Fig. S6, FTIR characterizations were conducted on the prepared membranes and CaF₂ nanocrystals, respectively, to examine their chemical structure. According to the FTIR spectrum of CaF₂, peaks at 472 and 780 cm^− 1 correspond to Ca-F stretching vibrations [32]. The mineral form of CaF₂ contains impurities that can be detected by various peaks. Regarding this, peaks at 518 and 1509 cm^− 1 are related to the bending modes of the Si-O bond [32, 33]. CaCO₃ impurity (less than 0.3%) is also represented by the peaks at 1425 cm^− 1 and 1617 cm^− 1 which are due to CO₃²⁻ stretching vibrations [32]. Another peak at 3442 cm^− 1 is associated with the H-O stretching vibration of impurities [32, 33].

In the spectra of membranes, various FTIR peaks were recorded. The peaks at 722 cm^− 1 and 949 cm^− 1 are related to the vibrations of C-H skeletons in the PE segment and the C-C stretching region, respectively [34, 35]. Additionally, C-H deformation vibration in PEBA can explain the peak at 779 cm^− 1. Further peaks were detected at 1095, 1206, 1241, and 1734 cm^− 1 due to the vibration of C-O in polymeric chains [34, 35]. The bending and stretching modes of the aliphatic C-H bond are indicated by the peaks at 1364, 1446, 1466, 2794, 2847, and 2918 cm^− 1 [34–36]. Additionally, the peaks at 1539, 1636, and 3309 cm^− 1 in the PA block can be explained by N-H deformation and C-N stretching, vibrations of the H-N-C = O bond, and H-N-O stretching vibration, respectively [18, 35].

Further investigation of Fig. S6 demonstrates that the FTIR spectra of prepared membranes changed by adding CaF₂. In detail, the intensity of the peaks at 472 and 779 cm^− 1 was increased due to the presence of more Ca-F bonds at higher concentrations of nanocrystals.

Crystalline structure

As illustrated in Fig. S7(a), the XRD spectrum of CaF₂ reveals prominent peaks at 2θ values of 28.4°, 47.1°, and 55.9°, corresponding to the (111), (220), and (311) reflections of the cubic structure (ICDD PDF Card No. 00-035-0816), confirming the presence of nanocrystalline CaF₂ [37]. Additionally, the presence of impurities was observed, evidenced by the peak at 2θ = 26.7° (SiO₂), along with other minor peaks [37].

XRD patterns of modified and unmodified PEBA membranes are also shown in Fig. S7(b). There are two main peaks in range of , the lower of which corresponds to the PA segment and the higher one to the PE segment [38]. The influence of CaF₂ nanocrystals on crystallinity, crystallite size, and d-spacing of the obtained membranes is also evaluated using XRD spectroscopy results.

The crystallinity degree of membranes is tabulated in Table S3. With the addition of CaF₂ nanocrystals, membrane crystallinity degree was reduced substantially from 23.1% in PEBA-0 to 16.44% in PEBA-1.5. The decreasing trend in could be related to the intrinsic behavior of nanocrystals and their effect as impurities or anti-nucleation agents, which postpone nucleation during membrane crystallization and reduce nucleation points [1, 39, 40]. Some studies reported that nanocrystals can disrupt polymer chain mobility, which may hinder the chain diffusion process, resulting in decreased crystallinity degree [40].

Figure S7(c) shows the average crystallite size of the fabricated membranes. By adding CaF₂ nanocrystals up to 1 wt%, the crystallite size was decreased from 147 Å in PEBA-0 to 78 Å in PEBA-1. Nanocrystals that act as impurities can prevent polymer packing and induce extra instability in crystal growth [41]. However, in PEBA-1.5, the crystallite size was increased due to the agglomeration of nanocrystals, which makes nanocrystals less effective in preventing chain packing and allows the crystal nuclei to grow more [41].

The average d-spacing of prepared membranes is also summarized in Fig. S7(c). With the addition of CaF₂ nanocrystals, the average distance between crystal plates was decreased from 4.25 Å in PEBA-0 to 3.89 Å in PEBA-1. This is due to the interaction of nanostructures and the polymer matrix [42], which results in dense polymer chains and a decrease in d-spacing. However, with the addition of a further amount of CaF₂ to the polymeric solution, due to nanocrystal agglomeration and reduced interfacial interaction between polymer chains and nanocrystals, the density of polymer chains decreased, leading to an increase in d-spacing of PEBA-1.5 to 4.14 Å [42, 43].

Thermal properties

Thermal properties of the prepared membranes are depicted in Table S3 and Fig. S8. Since rigid and soft segments of the PEBA polymer are thermodynamically incompatible, each segment exhibits its own and [38]. According to the DSC thermogram of the PEBA-0 membrane, PE and PA segments have values of -77.22 °C and 54.74 °C, similar to previous studies [30, 38]. Addition of 0.5 and 1 wt% CaF₂ nanocrystals to the polymeric solution increased the of PE and PA segments. The slight increase in of the mentioned nanocomposites can be attributed to the interaction between CaF₂ nanocrystals and polymer matrix, resulting in structural rigidity and limited polymer chain movements [23, 30]. In contrast, due to the agglomeration of nanocrystals within the polymer network and reduced interfacial interaction between the polymer chains and CaF₂, the of PE and PA segments in PEBA-1.5 decreased to -76.4 and 55.65 °C, respectively [44].

According to Table S3, the crystallinity degree of the prepared membranes decreased as the CaF₂ concentration increased from 0 to 1.5 wt%. Hence, , , and decreased from 28.68%, 3.43%, and 23.63%, respectively, for PEBA-0 to 17.39%, 2.09%, and 14.33%, respectively, for PEBA-1.5. The introduction of fillers contributed to the decrease in crystallinity because it can reduce polymer recrystallization affinity or disrupt polymer chain arrangement [40]. These results are in agreement with values calculated from the XRD pattern (Table S3).

Furthermore, the melting points of PEBA membranes are shown in Table S3. In this study, with the addition of 0.5 wt% CaF₂, the interaction between polymer chains increased due to the uniform dispersion of nanocrystals within the polymer matrix, resulting in a rigid structure with uniform heat transfer throughout the nanocomposite, which augmented the PE and PA melting points [45]. This approach is in accordance with similar reports [23, 30]. However, the polymeric membranes with a disordered structure and non-uniform heat transfer demonstrated a falling trend in due to nanocrystal agglomeration at high concentrations (1 and 1.5 wt%) [46]. This behavior can be seen in T_m values of PEBA-1 and PEBA-1.5.

Mechanical properties

During PV operation, the applied vacuum creates a pressure load on the membrane, making mechanical resistance a critical factor. Higher mechanical properties thus contribute to better durability and reliability under these conditions.

Three mechanical properties, including Young’s modulus, tensile stress, and elongation at break, were derived from the stress-strain data and are summarized in Table S4. It can be seen that increasing the concentration of CaF₂ nanocrystals from 0 to 1.5 wt% decreased the elongation at break from 422.68% for PEBA-0 to 97.97% for PEBA-1.5. In this case, the presence of CaF₂ nanocrystals in PEBA-0.5 and PEBA-1 contributed to stiffness and reduction of flexibility, resulting in a downward trend of elongation at break in the mentioned membranes [47]. The increased stiffness of PEBA-0.5 and PEBA-1 is consistent with data in DSC results (Table S3), which was augmented as CaF₂ loading increased from 0 to 1 wt%. Furthermore, extensive agglomeration of nanocrystals in PEBA-1.5 resulted in structural defects, explaining the lowest value of elongation at break [48].

According to Table S4, PEBA-0 exhibited the lowest Young’s modulus and tensile strength. These properties reached their maximum after adding 0.5 wt% CaF₂ to the polymeric solution. The uniform dispersion of nanocrystals at low concentrations results in strong interaction and compatibility between CaF₂ nanocrystals and polymer chains, which leads to the restriction of chain mobility and thus, enhanced mechanical properties of PEBA-0.5 [49]. However, with thorough agglomeration of CaF₂ at high concentrations, the interfacial adhesion between the nanocrystals and polymer decreased, resulting in a gradual reduction of Young’s modulus and tensile strength to 2.28 MPa and 10.60 MPa in PEBA-1.5, respectively [50]. Having said that, these two properties remained higher than those of PEBA-0 because incorporating inorganic nanoparticles into the polymer matrix increases Young’s modulus and tensile strength by crosslinking the polymer molecular chains [49].

PALS

The PALS technique was utilized to assess the free volume among the polymeric chains. In order to determine free volume parameters, , ,  R and  FFV were extracted from the PALS results. The obtained data, tabulated in Table S5, demonstrated that introducing 0.5 and 1 wt% CaF₂ nanocrystals into the membrane decreased and , resulting in a reduction of  R and  FFV between polymeric chains. It is noteworthy that adding fillers and the resultant polymer-filler interaction increase the rigidity of polymer chains, resulting in a denser structure with a lower  FFV [51]. It is also reported that the reduction of d-spacing (which was confirmed in Sect.  3.6) leads to a decrease in the free volume of the membrane crystalline Sects. [1, 52]. Furthermore, it is reported that FFV decreases as increases, which is in agreement with DSC results [30].

However, by adding a further amount of nanocrystals (1.5 wt%),  R and  FFV increased to 2.02 Å and 3.16% in PEBA-1.5, respectively, which can be explained by the agglomeration of CaF₂ and decrease in interfacial interaction between the nanocrystal and polymer, and thus, the improved mobility of polymer chains [40, 51].

Contact angle

The apparent and ideal water CA and glycerol CA are listed in Table S6. According to the results, loading the membrane with 0.5 wt% CaF₂ nanocrystals augmented the CAs, so that PEBA-0.5 exhibited the highest apparent water CA and glycerol CA, at 108.77° and 81.25°, respectively. The observed increase can be explained by the presence of fluorine groups on the membrane surface which enhances membrane hydrophobicity, and thus, increases its CA [15]. In contrast, by adding a further amount of CaF₂ (PEBA-1 and PEBA-1.5), the CAs decreased due to the agglomeration of CaF₂ nanocrystals and the reduction of their active surface area [53].

Furthermore, surface free energies (SFE) of water and glycerol tabulated in Table S6 demonstrates that the incorporation of 0.5 wt% CaF₂ decreased from 30.44 mJ/m² for PEBA-0 to 15.28 mJ/m² for PEBA-0.5. The previous literature reported that SFE decreases as CA and hydrophobicity increase [54]. However, SFEs increased by a further amount of nanocrystals (1 and 1.5 wt%) due to the agglomeration phenomenon [53, 54].

Hansen solubility parameters

It is known that the HSP distance () indicates the affinity and miscibility of two different components, with a higher revealing weaker affinity and a lower showing greater affinity and miscibility [18]. Here, a novel method was suggested to calculate the modified considering the agglomeration of nanofillers, and the obtained results including and modified are presented in Fig. 3. Based on Fig. 3, the between the membrane and PV feed (), water (), and 1-MEB () increased from 36719.06 pa^1/2, 36721.24 pa^1/2, and 8562.70 pa^1/2 in PEBA-0 to 37806.16 pa^1/2, 37806.84 pa^1/2, and 10265.22 pa^1/2 in PEBA-1.5, respectively.

Fig. 3.

∆ and modified ∆ for the prepared membranes: a. between the membrane and the PV feed, b. between the membrane and water, and c. between the membrane and 1-MEB

However, modified and modified increased with loading of 0.5 wt% nanocrystals and reached the maximum values of 36839.93 pa^1/2 and 36840.62 pa^1/2, respectively, indicating the lower affinity of PEBA-0.5 to water and PV feed. Increasing the CaF₂ concentration resulted in a downward trend in the modified and modified , implying the improved affinity of resultant membranes to water and PV feed. On the other hand, modified (Fig. 3(c)) dropped with the addition of 0.5 and 1 wt% nanocrystals, hitting a low of 8511.80 pa^1/2 for PEBA-1, demonstrating the higher affinity of 1-MEB to this membrane compared to the other membranes.

It is noteworthy that the modified values are in agreement with water CAs discussed in Sect.  3.10 because the agglomeration and dispersion of nanocrystals are taken into account in calculating the modified . However, unmodified values are not compatible with water CAs since CaF₂ agglomeration at higher concentrations does not affect this parameter.

To validate the predictive capability of the modified HSP approach, the modified HSP distances were correlated with two independently measured intrinsic membrane properties: water CA and DS. These properties were selected because they directly reflect the fundamental surface and bulk interactions between the membrane and feed components, and are governed primarily by polymer–penetrant affinity. As shown in Fig. S9, strong linear correlations were observed between the modified and water CA (R²= 0.91), as well as between the modified and DS (R²= 0.95). In stark contrast, the unmodified Bagley values showed no meaningful correlation with either property (R²= 0.07 for water CA and R²= 0.03 for DS), underscoring the necessity of incorporating the agglomeration effect into HSP calculations for nanocomposite membranes.

Swelling

The DS in the PV feed solution is depicted in Fig. S10. Among the prepared membranes, PEBA-0 and PEBA-0.5 showed the highest and lowest DS, at 25.99% and 12.5%, respectively. This behavior can be explained by the Flory-Renner theory. Based on their theory, the amount of Gibbs free energy required to swell a polymer equals the sum of the Gibbs free energy needed to mix the polymer with the solution (the solution that the polymer can absorb) and the Gibbs free energy required to cause a change in the elastic network [1]. Polymer-solution mixing Gibbs free energy can be related to HSP parameters and membrane miscibility with the feed solution [55]. In contrast, the Gibbs free energy required to change the elastic network depends on the membrane flexibility and Young’s modulus [1]. As discussed in Sect.  3.8, adding 0.5 wt% CaF₂ to PEBA-0 augmented Young’s modulus significantly, resulting in a more resistant elastic network. In addition, the high values of modified and (Fig. 3(a) and Fig. 3(b)) in PEBA-0.5 indicate the low miscibility of this membrane with feed and water, suggesting that incorporating up to 0.5 wt% nanocrystals reduces the DS. In addition, PEBA-0.5 showed the highest hydrophobicity (the highest apparent CA), which, according to the literature, gives rise to the lowest DS. In PEBA-1 and PEBA-1.5, DS increased due to reduced Young’s modulus and hydrophobicity, as well as lower modified and compared to PEBA-0.5, resulting in DS values of 17.02% and 25.04%, respectively. It can be seen that the DS of membranes (Fig. S10) are in agreement with modified values, while unmodified cannot interpret swelling results.

Sorption and diffusion selectivity

Figure S10 shows the calculated and values for each membrane. As can be seen, PEBA-1 represented the highest , at 73.68, which can be explained by considering two factors. Firstly, considering that PEBA-1 provided the lowest modified among the prepared membranes (Fig. 3), it can be concluded that this membrane has the highest affinity to 1-MEB. It should be noted that the agglomeration of nanocrystals is not considered in the calculation of unmodified and thus, cannot justify the variation of . Secondly, regarding AFM results, PEBA-1 possesses the roughest surface (highest in Table S2), resulting in a higher surface area in contact with the feed components and higher 1-MEB sorption [56].

Compared with the other prepared membranes, PEBA-1 accounted for the highest , at 859.52, which is due to its lowest FFV with high hydrophobicity and thus, suppressed water diffusion and enhanced 1-MEB diffusion through this membrane [57]. However, dropped in PEBA-1.5, which implies that water diffusion was facilitated and 1-MEB diffusion was restricted in these membranes. These variations in the diffusion of components can be attributed to the agglomeration of CaF₂ nanocrystals and the resultant lower FFV and hydrophobicity (lower water CA) of the mentioned membranes [57]. Furthermore, according to the Knudsen diffusion coefficient, agglomeration of CaF₂ nanocrystals at higher concentrations (1.5 wt%) results in complex and prolonged routes, which restrict the continuous facilitated transport of VOC molecules across the membrane and lead to a decrease in and PEBA-1.5 [58].

PV performance

Total flux

As shown in Fig. 4(a), PEBA-0 provided the highest and PEBA-1 accounted for the lowest total flux, at 724.68 and 31.25 g/m²h, respectively. This phenomenon is primarily caused by a sharp reduction in FFV with loading of 1 wt% nanocrystals [59]. Hence, PEBA-1 offers a smaller hole radius in comparison with other membranes (Table S5), leading to suppressed diffusion of molecules and lower total flux [60]. It should also be noted that cracks and defects caused by nanoparticle agglomeration create new pathways for the transport of feed components through the membrane, resulting in an increase in the total flux of PEBA-1.5 to 421.25 g/m²h [61].

Fig. 4.

PV performance of the prepared membranes: a. total flux, b. separation factor, c. water and 1-MEB flux and d. PSI

Separation factor

As shown in Fig. 4(b), adding CaF₂ nanocrystals to PEBA increased the separation factor in PEBA-0.5 and PEBA-1 to 913.45 and 63330.16, respectively. PEBA-0.5 and PEBA-1 demonstrated higher separation factors due to their higher hydrophobicity, lower DS, and enhanced compared to PEBA-0. Nevertheless, PEBA-1 achieved the highest separation factor owing to its superior , which plays a critical role in the separation performance [62]. However, the decreased separation factor in PEBA-1.5 can be related to nanocrystal agglomeration, which lowers the hydrophobicity of the membrane, increases its DS, and decreases its and .

Water flux

According to the partial flux data reported in Fig. 4(c), the PEBA-0 membrane represented the highest water flux (721.5 g/m²h), while increasing the loading of CaF₂ nanocrystals dramatically decreased the water flux, reaching the lowest value at 7.5 g/m²h in PEBA-1. However, at further CaF₂ loading (1.5 wt%), water flux increased significantly to 418.43 g/m²h, still lower than PEBA-0. The overall decrease in water flux of CaF₂ nanocomposite membranes can be attributed to the augmented hydrophobicity (increased CA) and lower DS of these nanocomposites [57]. Furthermore, the general decreasing trend of FFV in nanocomposite membranes is in accordance with the trend of water flux variations [58, 59]. Among these samples, PEBA-1 exhibited high hydrophobicity and low DS, together with the lowest FFV and high rigidity, thereby yielding the lowest water flux [58]. However, the increased water flux of PEBA-1.5 can be attributed to an increase in FFV and DS, along with a decrease in its hydrophobicity [58, 59].

VOC flux

The flux of 1-MEB through the membrane can be interpreted considering water CA [57] (Table S6), modified (Fig. 3(c)), and [28] (Fig. S10). The PEBA-0 membrane exhibited the lowest 1-MEB flux, at 3.5 g/m²h, while adding CaF₂ nanocrystals up to 1 wt% and the resultant increase in the hydrophobicity of nanocomposite membranes, the VOC flux improved, and the maximum VOC flux (23.75 g/m²h) was observed for PEBA-1 (Fig. 4(c)). Although PEBA-0.5 showed the highest hydrophobicity, the essential factor for the transfer of components within PV membranes is [62]. Since PEBA-1 provided the highest and thus has the highest affinity to 1-MEB (the lowest value of modified ), this membrane exhibited a higher VOC flux compared to PEBA-0.5. From another viewpoint, the surface roughness () of PEBA-1 is higher than the other prepared membranes. As a result, it has a larger surface area in contact with the feed components, resulting in enhanced 1-MEB sorption and augmented 1-MEB flux [57]. The decrease in VOC flux of PEBA-1.5 compared to PEBA-1 and PEBA-0.5 can be related to lower hydrophobicity of the former, as well as agglomeration of nanocrystals in this membrane. It should be noted that the VOC fluxes obtained in this study are in agreement with the trend of variation (Fig. 3(c)), while unmodified cannot explain the results.

PSI

According to Fig. 4(d), PEBA-0 demonstrated the lowest PSI, at 59,068 g/m²h, while adding CaF₂ nanocrystals generally improved the PSI. Among the nanocomposite membranes, PEBA-1 showed the highest PSI due to its highest separation factor. Furthermore, the decrease in PSI of PEBA-1.5 to 56,354 g/m²h can be attributed to a sharp decrease in the separation factor of this membrane.

Proposed separation mechanism

To further elucidate the transport mechanism, the PALS-derived FFV was directly compared with the PV performance. The PEBA-1 membrane exhibited the lowest FFV (2.95%), indicating that the incorporation of well-dispersed CaF₂ nanocrystals promoted tighter polymer chain packing through favorable polymer–filler interactions. Correspondingly, the water flux decreased sharply from 721.5 to 7.5 g m⁻² h⁻¹, demonstrating that water diffusion was effectively suppressed. In contrast, the same membrane exhibited the highest 1-MEB flux (23.75 g m⁻² h⁻¹) and the highest separation factor (63,330.2). These results indicate that CaF₂ does not merely function as an adsorptive filler but modifies the polymer microstructure to create highly selective transport pathways, in which water diffusion is significantly hindered while the preferential sorption and diffusion of 1-MEB are maintained.

In addition, selective transport behavior of PEBA-1 cannot be attributed to the formation of non-selective interfacial voids between the CaF₂ nanocrystals and the PEBA matrix. High-magnification FESEM observations revealed intimate contact between the nanocrystals and the surrounding polymer without detectable interfacial gaps. This observation is further supported by the PALS results, as the lowest FFV observed for PEBA-1 indicates densification of the polymer network rather than void formation. Moreover, the formation of interfacial voids would be expected to facilitate the permeation of both water and 1-MEB through non-selective diffusion pathways. Instead, water permeation was dramatically suppressed while the separation factor reached its maximum value, confirming that mass transport is predominantly governed by selective sorption and diffusion rather than leakage through interfacial defects. Therefore, the superior separation performance of PEBA-1 can be attributed to the synergistic effects of optimized polymer chain packing, enhanced membrane hydrophobicity, and the stronger affinity of 1-MEB predicted by the modified HSP analysis.

Effect of feed temperature on membrane performance

In this study, the relationship between operating temperature and the separation efficiency of the PEBA-1 membrane was investigated. The operation temperature ranged from 25 °C to 75 °C, using a 50 ppm 1-MEB solution. As depicted in Fig. S11(a) and S11(b) the fluxes of individual components (water and 1-MEB), as well as the separation factor and total flux of all membranes, exhibited a consistent upward trend with increasing operation temperature, consistent with previous research findings [63]. Specifically, the total permeate flux increased from 31.25 to 1028.17 g/m²h, while the separation factor decreased from 63330.16 to 2068.02. This trend can be attributed to the rise in the operational temperature, which enhances the mobility of the polymeric matrix [63], thereby increasing free volume and facilitating the diffusion of components, consequently boosting the total flux [64]. However, due to their smaller size, water molecules permeate more easily than 1-MEB molecules which results in a higher water content in the permeate, diluting the desired component significantly and leading to a lower separation factor [44].

The influence of operating temperature on permeation flux could also be interpreted using an Arrhenius-type relationship and its plots (Fig. S11(c)) as follows [64]:

19

In this equation, J_p (g/(m²h)) refers to the permeation flux, while J₀, E_p (J/mol), R (J/(mol·K)), and T stand for the pre-exponential constant, activation energy, universal gas constant, and absolute temperature (K), respectively.

According to this relationship, higher values of indicate that flux becomes more sensitive to temperature variation [64]. For PEBA-1, the activation energies for the permeating components in feed solution followed the order water > 1-MEB. This ordering suggests that water permeation is the most temperature-dependent during the PV separation process. As a result, the water flux increased more rapidly with temperature, which consequently led to a reduction in the separation factor to 2068.02 at 75 °C, as previously shown in Fig. S11(a).

Effect of feed concentration on membrane performance

Figure S12 illustrates the impact of 1-MEB concentration on the separation performance of the PEBA-1 membrane. As the concentration of 1-MEB increased from 20 to 50 ppm, both the total flux (Figure S12(a)), and water flux (Figure S12(b)), exhibited a consistent improvement, with the total flux increasing from 6.6 to 31.25 g/m²h. Conversely, the separation factor of PEBA-1 increased from 2850.94 to 63330.16 with the increase in 1-MEB concentration (Figure S12(a)). The augmentation of 1-MEB concentration could induce a certain DS in the hydrophobic PEBA-1 membrane, making the polymeric chains more flexible and consequently enhancing the total flux [63]. Additionally, the increase in 1-MEB concentration can amplify the driving force for transmembrane transport of molecules, which may be particularly advantageous for the transport of 1-MEB and water molecules [63]. Thus, there was a rising trend in the total flux, and separation factor (Figure S12(a)).

Comparison of PV results with previous studies

The PV performance of the PEBA/CaF₂ membranes was first evaluated by comparison with neat polymeric membranes and their nanocomposites for 1-MEB removal (Table S7). The incorporation of 1 wt% CaF₂ increased the separation factor from 82.51 (PEBA-0) to 63,330.16 and enhanced the PSI from 59,068 to approximately 1.97 × 10⁶ g/m²h, representing a 33-fold improvement in overall separation efficiency. To further contextualize this performance, the PEBA-1 membrane was benchmarked against recently reported PEBA-based mixed matrix membranes incorporating advanced fillers such as ZIF-8, MIL-101, and fluorinated MOFs (Table S8). The PEBA-1 membrane achieved a PSI of 1.97 × 10⁶ g/m²h, surpassing all listed systems and exhibiting a value approximately 13-fold higher than the best-performing competing membrane (PEBA/ZIF-8, PSI = 153,118 g/m²h). This exceptional selectivity-driven performance reflects the intrinsic hydrophobicity of CaF₂, which suppresses water permeation to an unprecedented extent (7.5 g/m²h) while maintaining selective VOC transport (23.75 g/m²h), thereby demonstrating the strong practical competitiveness of the proposed membrane for dilute VOC recovery.

Long-term stability

To evaluate the operational stability of the optimal membrane under continuous PV conditions, a long-term test was conducted on the PEBA-1 membrane over 50 h at 50 ppm 1-MEB feed concentration and 25 °C. As shown in Fig. 5, both the total flux and separation factor remained remarkably stable throughout the test period. The total flux fluctuated slightly around an average value of approximately 31.5 g/m²h (variation ≈ 5%), while the separation factor maintained a consistently high value around 63,300 (variation < ± 0.1%). The absence of significant performance degradation indicates that the PEBA-1 membrane possesses excellent structural integrity and stable interfacial properties under continuous hydrophobic PV conditions. These results suggest that the membrane is promising for practical, long-term industrial applications in dilute VOC recovery.

Fig. 5.

Long-term stability of the PEBA-1 membrane during continuous PV of 1-MEB (50 ppm) at 25 °C over 50 h

Conclusion

In this study, PEBA/CaF₂ nanocomposite membranes were fabricated for the first time for the removal of 1-MEB from water via hydrophobic PV. To bridge the gap between theoretical solubility parameters and the actual morphology of nanocomposite membranes, a modified Bagley relationship was introduced that incorporates the Suetsugu D_i to account for nanofiller agglomeration. This approach was quantitatively validated against independent experimental data, with modified HSP distances showing strong correlations with water CA (R² = 0.91) and DS (R² = 0.95). In contrast, unmodified Δ values exhibited poor correlations with these properties, confirming that ideal filler dispersion assumptions are practically inadequate for nanocomposite systems. With the incorporation of CaF₂ nanofiller, the membranes became more resistant to water diffusion, resulting in lower swelling degrees and enhanced sorption and diffusion selectivity for 1-MEB. Among the prepared membranes, PEBA-1 provided the highest α_sorp (73.68), consistent with the lowest modified Δ_m,1-MEB. This membrane also achieved the highest 1-MEB flux (23.75 g/m²h) and separation factor (63,330.16), as well as the lowest water flux (7.5 g/m²h). These results underscore the potential of PEBA/CaF₂ nanocomposite membranes for efficient VOC–water separations.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Amirreza Malekzadeh Dirin: Investigation, Data curation, Writing - Original Draft.Ehsan Saljough: Supervision, Project administration, Review & Editing.Seyed Mahmoud Mousavi: Supervision, Review & Editing.Shirin Kiani: Investigation, Review & Editing.Salma Ghorab: Investigation, Review & Editing.

Funding

This research received no external funding and was conducted without any financial support from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethical Approval

Not applicable.

Consent to Participate

Not applicable.

Consent to Publish

Not applicable.

Competing interests

The authors declare no competing interests.